I'm having trouble understanding congruency between Triangles.. Like SSS, SAS, ASA, and AAS. Can anyone help..?

Sure. There's basically a bunch of ways to prove that triangles are congruent. Congruent means that all the sides and all the angles are EXACTLY the same.
For example: SSS is one way of proving that 2 triangles are congruent. SSS means "side side side", meaning if the three sides of two triangles are the same, then the two triangles are congruent. This means that if I gave you one triangle with side lengths and angles, and gave you another triangle with only side lengths, and all the side lengths were identical, you could use the angles of the first triangle to know the angles for the second.
ASA means "angle side angle". So if you can find 2 identical angles, followed by 2 identical sides, followed by 2 identical angles (in order) then the triangles will be congruent.
And so on

side side side
side angle side
angle side angle
angle angle side
all conditions in solving for triangles
IT CAN NEVER be Angle angle angle.
You need at least one side and one angle to solve a triangle typed equation.

Thank you very much, first off. But I'm kind of confused on the definition of "AAS" because it states, "If two angles and a non-included side are congruent to the corresponding two angles and side of a second triangle, the two triangles are congruent." Does that just mean if both of the triangles have two angles and a non-included side that are the same size, they're congruent?